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Study Of A Relativistic Quantum Harmonic Oscillator By The Method Of State-Dependent Diagonalization

Author

Listed:
  • H. C. LEE

    (Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

  • K. L. LIU

    (Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

  • C. F. LO

    (Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

Abstract

We apply the method of State-dependent Diagonalization to study the eigenstates of the relativistic quantum harmonic oscillator in the low relativistic limit. The relativistic corrections of the energy eigenvalues of the quantum harmonic oscillator are evaluated for different values of the relativistic parameterα ≡ ħω0/ m0c2. Unlike the conventional exact diagonalization, this new method is shown to be very efficient for evaluating the energy eigenvalues and eigenfunctions. We have also found that for non-zero α the eigenfunctions of the system become more localized in space and that the ground state of the SHO (i.e., theα = 0case) turns into a squeezed state. Furthermore, since our system is a special case of the quantum harmonic oscillator with a velocity-dependent anharmonic potential, this new approach should be very useful for investigating the cases with more complicated velocity-dependent anharmonic potentials.

Suggested Citation

  • H. C. Lee & K. L. Liu & C. F. Lo, 1996. "Study Of A Relativistic Quantum Harmonic Oscillator By The Method Of State-Dependent Diagonalization," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 645-653.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:05:n:s0129183196000545
    DOI: 10.1142/S0129183196000545
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